Bechoros 19b: If one buys an animal from a non-Jew and does not know if it has ever given birth in the past…

Bechoros 21b: If one buys an animal from a Jew, and the Jew does not tell him whether the animal has previously given birth, and now it gives birth, is the baby a bechor? Rav said: It is certainly a bechor, because if the animal had previously given birth, the seller would have boasted about it.

Taz Yoreh Deah 316:4: If a non-Jew is selling a cow and the Jew tells him that the younger it is, the more he will pay for it, and the non-Jew says it has already had four calves, he is believed, because if it had been a cow that never gave birth, he would have said so, for his own gain.

בכורות יט ע”ב: הלוקח בהמה מן העובד כוכבים, ואינו יודע אם ביכרה אם לא ביכרה וכו’

בכורות כא ע”ב: איתמר. מצינו לוקח מעובד כוכבים, לוקח מישראל מאי? אמר רב: בכור ודאי, דאם איתא דבכרה ־ אישתבוחי הוה מישתבח ליה.

Rav Yisroel Belsky once allowed a kashrus agency to rely on non-Jewish workers in checking eggs for blood spots by offering a financial reward to the workers for every egg that they found containing a blood spot.  Eventually, the innovation was discontinued. Apparently, one of the company workers was a diabetic who carried around a lancet.  The incidence of blood found in eggs was significantly higher during this period. 

Source: https://vinnews.com/2022/11/24/adrianna-the-non-jewish-nanny-and-halacha/

Bechoros 24b: Rabbi Yossi ben Hameshulam says: When slaughtering a bechor offering, one should push aside the hair with the knife to uncover the place of shechitah, and one is even allowed to pull out the hair (and it is not forbidden under the prohibition of shearing a bechor). Rabbi Asi said in the name of Resh Lakish: It is only permitted to pull out the hair by hand. But it says with the knife! – Change the words of the Mishnah from “with the knife” to “for the knife”.

רבי יוסי בן המשולם אומר: השוחט את הבכור ־ עושה מקום בקופיץ מיכן ומיכן ותולש את השער. אמר רב אסי אמר ריש לקיש: לא שנו אלא ביד, אבל בכלי אסור. והקתני: עושה מקום בקופיץ מיכן ומיכןִ! תני: לקופיץ.

Someone once asked R’ Chaim Kanievsky, “When I go to put a sefer away on the shelf, and the other seforim are packed closely together, am I allowed to use the sefer in my hand to push the others to the side and make room, or is that a disgrace to the sefer?”

To the questioner’s surprise, R’ Chaim replied, “It is an explicit Mishnah in Bechoros that one may do this. It says that one may use the knife, which is a holy vessel of the Beis Hamikdash, to push aside the hair of a korban. Although the Gemara modifies the text, that is only because pulling out hair using the knife would be forbidden. But using the knife to push aside the hair is permitted. So we see that this is called using a holy object for a holy purpose, since it is a preparation for the avodah. Here too, pushing aside the other seforim is a preparation for putting the sefer back and is permitted.”

He added, “One could ask a similar question about using one’s tefillin to push his shirt sleeve up to make room for the tefillin. And the answer is that it is permitted, as we said.”

Source: Divrei Siach, Vayechi 5781